Question

In MATLAB

At time t=0 when a rocket's engine shuts down, the rocket has reached an altitude of 500 m and is rising at a velocity of 125 m/s. The height of the rocket as a function of time is 9.8 h(t)= t? +125t+500 for t > 0 2 Create a time array t from O sec to 30 sec with an increment of 1 sec and a corresponding array for the height h. Plot the height of the rocket from 0 to 30 seconds using the command plot, and estimate the time and the height of the rocket when it reaches the maximum height using [time, hmax]=ginput (1). Note that a separate plot window will be open for ginput. Use the disp command to output time and maximum height using num2str(num). The following is a sample output. The time the rocket reaches the maximum height is 12.8341 sec, and its height is 1295.7198 meters

Answer 1

Solution:

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The following is the MATLAB program that plots the height of the rocket from 0 to 30 seconds, and using the ginput function, it estimates the maximum height the rocket reaches and the time when the rocket hits the ground: clear all close all clc t=0:30; h_t=(-(9.8/2).*t.^2)+(125.*t) +500; plot(t, h_t); title('Horizontal path of the rocket'); xlabel('time, t--->'); ylabel('height,h(t)--->'); [x, y]=ginput(1); disp (['The maximum height of the rocket is ' num2 str(y)]); [x1, y1]=ginput (1): disp (['The time at which rocket reaches to ground is num2 str(x1)])

The following is the MATLAB plot for the horizontal path of the rocket: Horizontal path of the rocket 1400 1200 1000 800 height,h(t)---> 600 400 200 0 -200 5 10 20 25 30 15 time,t--->

Pick the point on the graph where the rocket reaches maximum height as follows: х Figure 1 File Edit View Insert Tools Desktop Window Help Horizontal path of the rocket 1400 1200 1000 800 height,h(t)---> 600 400 200F 0 -200 0 תש 10 20 25 30 15 time,t--->

х Figure 1 File Edit View Insert Tools Desktop Window Help Horizontal path of the rocket 1400 1200 1000 800 height, h(t)---> 600 400 200 8 1 -200 0 5 10 20 25 30 15 time,t--->

The time the rocket reaches the maximum height is 12.8341 sec, and its height is 1295.7198 meters